Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish. Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group:

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish. The composition parameters (\(P_{(pelagic)ayu}\), \(P_{(black|pelagic)ayu}\), \(P_{(yelloweye|non-pelagic)ayu}\)) were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping (pelagic or yelloweye), \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases calculated from the sum of the user group releases. The proportion of total rockfish harvested by user group, \(pH_{ayu}\), was assumed to be the mean of \(pH_{(pelagic)ayu}\), \(pH_{(yelloweye)ayu}\) and \(pH_{(nonpel-nonYE)ayu}\) weighted by the relative harvest \(H_{(comp)ayu}\) such that

\[\begin{equation} R_{ayu}~=~ \frac{\sum ({H_{(comp)ayu} * pH_{(comp)ayu})}}{\sum {H_{(comp)ayu}}} \end{equation}\]

The proportion harvest parameters \(pH_{(pelagic)ayu}\) and \(pH_{(yelloweye)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{ayuc})~=~\beta1_{(pH)ayuc} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc}))) + \beta34_{(pH)ayuc}} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

\(pH_{(nonpel-nonYE)ayu}\) was modeled separately with an informative prior centered around a \(pH\) of 0.8 such that

\[\begin{equation} pH_{(nonpel-nonYE)ayu}~\sim~\textrm{beta}(in development) \end{equation}\]

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \end{equation}\]

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modelled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \end{equation}\]

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modelled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

**Figure 13.**- Annual proportion of all rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of all rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta2_pelagic 2 1.424752
tau_beta0_pH 2 1.318385
beta1_pelagic 1 1.174656
parameter n badRhat_avg
tau_beta0_yellow 1 1.153438
beta0_pelagic 1 1.131718
Table 2. Summary of unconverged parameters by area
CI NG PWSI PWSO SSEO
beta0_pelagic 0 0 0 1 0
beta1_pelagic 0 1 0 0 0
beta2_pelagic 0 1 0 0 1
tau_beta0_pH 1 0 1 0 0
tau_beta0_yellow 1 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.157 0.070 -0.288 -0.157 -0.017
mu_bc_H[2] -0.121 0.039 -0.190 -0.123 -0.035
mu_bc_H[3] -0.466 0.067 -0.589 -0.469 -0.326
mu_bc_H[4] -1.147 0.217 -1.590 -1.145 -0.740
mu_bc_H[5] 0.561 0.625 -0.323 0.474 2.081
mu_bc_H[6] -2.220 0.314 -2.823 -2.224 -1.623
mu_bc_H[7] -0.478 0.112 -0.704 -0.476 -0.270
mu_bc_H[8] 0.157 0.395 -0.524 0.129 0.938
mu_bc_H[9] -0.325 0.130 -0.586 -0.327 -0.072
mu_bc_H[10] -0.130 0.065 -0.253 -0.132 0.007
mu_bc_H[11] -0.131 0.036 -0.202 -0.131 -0.060
mu_bc_H[12] -0.268 0.111 -0.511 -0.260 -0.068
mu_bc_H[13] -0.152 0.077 -0.301 -0.154 0.003
mu_bc_H[14] -0.327 0.096 -0.517 -0.324 -0.144
mu_bc_H[15] -0.360 0.048 -0.454 -0.360 -0.266
mu_bc_H[16] -0.349 0.379 -0.988 -0.384 0.468
mu_bc_R[1] 0.354 0.763 -1.285 0.400 1.761
mu_bc_R[2] -0.171 0.593 -1.346 -0.173 0.933
mu_bc_R[3] -0.460 0.496 -1.515 -0.418 0.405
mu_bc_R[4] -1.190 0.846 -2.545 -1.307 0.857
mu_bc_R[5] 1.546 0.712 0.022 1.575 2.812
mu_bc_R[6] 0.639 0.591 -0.642 0.675 1.693
mu_bc_R[7] 1.222 1.235 -1.434 1.249 3.104
mu_bc_R[8] 2.326 0.682 0.564 2.458 3.268
mu_bc_R[9] 2.507 1.258 -0.290 2.538 4.447
mu_bc_R[10] 1.336 1.148 -1.252 1.454 3.240
mu_bc_R[11] 0.502 0.233 0.017 0.506 0.953
mu_bc_R[12] -0.912 0.583 -1.910 -0.972 0.487
mu_bc_R[13] 0.113 0.271 -0.402 0.105 0.671
mu_bc_R[14] 0.110 0.331 -0.578 0.117 0.742
mu_bc_R[15] -0.023 0.249 -0.518 -0.002 0.405
mu_bc_R[16] 0.685 0.311 0.038 0.702 1.281
tau_pH[1] 378429.572 7391994.329 76.096 774.569 336004.747
tau_pH[2] 1.448 0.168 1.141 1.441 1.797
beta0_pH[1,1] 0.076 0.949 -2.067 0.120 1.838
beta0_pH[2,1] 0.489 0.755 -1.075 0.507 1.914
beta0_pH[3,1] -0.291 0.967 -2.431 -0.173 1.333
beta0_pH[4,1] 0.196 1.433 -2.476 0.134 3.620
beta0_pH[5,1] 2.348 2.677 -0.564 2.001 6.678
beta0_pH[6,1] 2.697 2.549 -0.368 2.028 8.360
beta0_pH[7,1] 2.255 2.841 -1.519 1.802 8.368
beta0_pH[8,1] 1.824 1.388 -0.770 1.783 4.380
beta0_pH[9,1] 2.765 3.625 -1.297 2.101 7.890
beta0_pH[10,1] 1.388 1.245 -1.425 1.495 3.547
beta0_pH[11,1] -1.534 0.634 -2.714 -1.497 -0.362
beta0_pH[12,1] -1.333 0.790 -2.713 -1.352 0.414
beta0_pH[13,1] -1.288 0.721 -2.705 -1.262 0.165
beta0_pH[14,1] -1.499 0.692 -2.710 -1.499 -0.084
beta0_pH[15,1] -1.657 0.603 -2.709 -1.638 -0.540
beta0_pH[16,1] -1.596 0.651 -2.721 -1.582 -0.310
beta0_pH[1,2] 2.508 0.348 1.829 2.538 3.068
beta0_pH[2,2] 2.720 0.346 1.889 2.775 3.228
beta0_pH[3,2] 2.453 0.379 1.689 2.475 3.119
beta0_pH[4,2] 2.590 0.329 1.731 2.645 3.055
beta0_pH[5,2] 3.426 1.590 1.555 3.142 7.014
beta0_pH[6,2] 2.776 0.388 1.985 2.806 3.410
beta0_pH[7,2] 1.659 0.943 -1.656 1.923 2.391
beta0_pH[8,2] 2.596 0.632 0.763 2.751 3.195
beta0_pH[9,2] 2.866 0.644 1.540 2.967 3.778
beta0_pH[10,2] 3.052 0.835 1.156 3.224 4.127
beta0_pH[11,2] -2.734 0.024 -2.750 -2.742 -2.668
beta0_pH[12,2] -2.729 0.032 -2.750 -2.740 -2.640
beta0_pH[13,2] -2.730 0.031 -2.750 -2.740 -2.651
beta0_pH[14,2] -2.733 0.024 -2.750 -2.741 -2.668
beta0_pH[15,2] -2.731 0.028 -2.750 -2.740 -2.650
beta0_pH[16,2] -2.730 0.030 -2.750 -2.740 -2.646
beta1_pH[1,1] 2.459 0.824 1.308 2.291 4.496
beta1_pH[2,1] 1.069 0.496 0.564 0.962 2.457
beta1_pH[3,1] 1.648 0.768 0.164 1.639 3.193
beta1_pH[4,1] 1.607 1.076 0.203 1.409 4.541
beta1_pH[5,1] 2.588 1.525 0.289 2.360 6.270
beta1_pH[6,1] 4.597 2.271 0.526 4.731 8.955
beta1_pH[7,1] 3.144 1.833 0.229 3.121 6.777
beta1_pH[8,1] 2.767 1.081 1.264 2.554 5.560
beta1_pH[9,1] 1.643 1.004 0.236 1.539 4.362
beta1_pH[10,1] 1.093 0.230 0.702 1.078 1.567
beta1_pH[11,1] 3.652 0.570 2.642 3.611 4.812
beta1_pH[12,1] 1.767 0.496 0.977 1.700 2.848
beta1_pH[13,1] 2.799 0.603 1.743 2.746 4.077
beta1_pH[14,1] 2.460 0.572 1.383 2.433 3.612
beta1_pH[15,1] 2.463 0.590 1.288 2.467 3.584
beta1_pH[16,1] 4.359 0.669 3.118 4.338 5.709
beta1_pH[1,2] 1.454 1.148 0.110 1.231 4.831
beta1_pH[2,2] 1.503 1.565 0.052 0.898 5.855
beta1_pH[3,2] 1.239 0.566 0.253 1.205 2.289
beta1_pH[4,2] 2.044 1.870 0.070 1.339 6.853
beta1_pH[5,2] 3.176 1.937 0.202 2.924 7.762
beta1_pH[6,2] 1.900 1.174 0.275 1.694 4.994
beta1_pH[7,2] 2.064 1.874 0.056 1.445 6.707
beta1_pH[8,2] 1.597 1.607 0.053 1.025 5.947
beta1_pH[9,2] 1.670 1.341 0.113 1.383 5.520
beta1_pH[10,2] 1.698 1.400 0.111 1.357 5.545
beta1_pH[11,2] 4.643 0.231 4.189 4.644 5.090
beta1_pH[12,2] 4.809 0.339 4.207 4.795 5.510
beta1_pH[13,2] 5.259 0.244 4.782 5.255 5.736
beta1_pH[14,2] 4.706 0.252 4.230 4.707 5.201
beta1_pH[15,2] 5.274 0.231 4.822 5.273 5.738
beta1_pH[16,2] 5.456 0.233 5.002 5.451 5.909
beta2_pH[1,1] 0.338 0.592 0.086 0.224 1.439
beta2_pH[2,1] 1.839 1.845 0.100 1.186 6.706
beta2_pH[3,1] 2.940 2.332 -1.952 2.707 7.849
beta2_pH[4,1] 1.622 2.801 -4.800 1.530 7.095
beta2_pH[5,1] 2.627 2.293 -1.386 2.266 7.671
beta2_pH[6,1] 2.856 2.123 0.074 2.514 7.704
beta2_pH[7,1] -1.401 3.595 -7.075 -2.296 6.116
beta2_pH[8,1] 1.676 1.763 0.128 0.979 6.511
beta2_pH[9,1] 2.384 2.640 -3.634 2.263 7.924
beta2_pH[10,1] 2.326 1.774 0.347 1.804 7.009
beta2_pH[11,1] 0.989 0.675 0.419 0.805 3.060
beta2_pH[12,1] 2.494 2.013 0.161 1.952 7.337
beta2_pH[13,1] 1.970 1.657 0.338 1.366 6.652
beta2_pH[14,1] 3.588 1.954 0.784 3.274 7.983
beta2_pH[15,1] 2.954 1.943 0.461 2.503 7.547
beta2_pH[16,1] 0.486 0.384 0.208 0.408 1.188
beta2_pH[1,2] 0.881 2.915 -6.115 1.187 5.877
beta2_pH[2,2] -1.585 2.840 -7.121 -1.502 4.622
beta2_pH[3,2] -2.799 2.311 -7.920 -2.461 1.353
beta2_pH[4,2] -2.388 2.692 -7.785 -2.252 3.581
beta2_pH[5,2] 0.693 2.954 -5.937 0.909 6.129
beta2_pH[6,2] -2.359 2.258 -7.424 -1.980 1.643
beta2_pH[7,2] -2.088 2.932 -7.660 -2.128 4.180
beta2_pH[8,2] -1.497 3.061 -7.310 -1.599 4.760
beta2_pH[9,2] -2.070 2.879 -7.661 -2.110 4.184
beta2_pH[10,2] -0.535 3.247 -7.148 -0.120 5.367
beta2_pH[11,2] -5.026 1.906 -9.377 -4.825 -1.992
beta2_pH[12,2] -1.859 1.220 -5.322 -1.495 -0.609
beta2_pH[13,2] -3.766 1.724 -8.095 -3.413 -1.404
beta2_pH[14,2] -3.393 1.697 -7.654 -2.999 -1.263
beta2_pH[15,2] -5.112 1.817 -9.178 -4.882 -2.201
beta2_pH[16,2] -5.463 1.805 -9.372 -5.283 -2.518
beta3_pH[1,1] 36.928 2.799 31.995 36.658 43.032
beta3_pH[2,1] 35.950 1.968 32.548 35.930 40.570
beta3_pH[3,1] 32.080 3.426 22.373 32.741 38.563
beta3_pH[4,1] 34.747 6.007 21.124 36.510 42.677
beta3_pH[5,1] 37.197 5.521 22.145 39.147 43.680
beta3_pH[6,1] 33.242 6.267 19.621 35.907 40.375
beta3_pH[7,1] 25.683 7.331 19.358 20.728 41.767
beta3_pH[8,1] 32.866 2.477 28.530 32.998 37.994
beta3_pH[9,1] 29.367 4.255 21.447 29.096 41.050
beta3_pH[10,1] 34.828 1.153 32.115 34.971 36.599
beta3_pH[11,1] 29.284 0.844 27.368 29.372 30.682
beta3_pH[12,1] 30.317 2.321 26.607 29.900 35.681
beta3_pH[13,1] 32.597 0.999 30.496 32.606 34.345
beta3_pH[14,1] 30.434 0.821 28.860 30.510 31.695
beta3_pH[15,1] 31.480 1.976 26.939 31.675 34.605
beta3_pH[16,1] 31.458 1.253 28.648 31.523 33.733
beta3_pH[1,2] 36.022 7.399 20.357 39.902 43.626
beta3_pH[2,2] 29.104 6.475 19.510 27.993 41.913
beta3_pH[3,2] 40.246 4.544 24.099 41.576 43.745
beta3_pH[4,2] 28.564 7.000 19.601 26.122 42.706
beta3_pH[5,2] 30.264 6.431 19.760 29.818 42.558
beta3_pH[6,2] 33.610 4.172 21.846 34.747 40.568
beta3_pH[7,2] 27.075 5.623 19.304 26.259 39.660
beta3_pH[8,2] 28.488 6.015 19.549 27.667 41.781
beta3_pH[9,2] 33.844 8.548 19.860 33.318 43.923
beta3_pH[10,2] 29.585 6.529 19.696 28.417 42.012
beta3_pH[11,2] 43.206 0.220 42.720 43.210 43.615
beta3_pH[12,2] 42.116 0.611 40.731 42.150 43.128
beta3_pH[13,2] 43.374 0.249 42.891 43.365 43.848
beta3_pH[14,2] 42.797 0.365 41.974 42.873 43.374
beta3_pH[15,2] 43.315 0.185 42.972 43.304 43.680
beta3_pH[16,2] 43.368 0.179 43.054 43.356 43.737
beta0_pelagic[1] 1.434 0.614 0.202 1.475 2.358
beta0_pelagic[2] 1.239 0.288 0.456 1.299 1.649
beta0_pelagic[3] 0.139 0.353 -0.814 0.200 0.633
beta0_pelagic[4] 0.126 0.483 -0.975 0.204 0.747
beta0_pelagic[5] 0.596 0.463 -0.627 0.688 1.230
beta0_pelagic[6] 0.585 0.491 -0.542 0.659 1.350
beta0_pelagic[7] 1.498 0.176 1.150 1.497 1.833
beta0_pelagic[8] 1.631 0.213 1.062 1.653 1.947
beta0_pelagic[9] 1.646 0.666 0.076 1.782 2.537
beta0_pelagic[10] 2.110 0.567 0.723 2.288 2.809
beta0_pelagic[11] -0.481 0.530 -1.805 -0.405 0.296
beta0_pelagic[12] 1.647 0.160 1.330 1.654 1.949
beta0_pelagic[13] 0.272 0.235 -0.297 0.306 0.639
beta0_pelagic[14] -0.189 0.315 -0.876 -0.158 0.294
beta0_pelagic[15] -0.304 0.140 -0.586 -0.303 -0.038
beta0_pelagic[16] -0.095 0.318 -0.830 -0.054 0.399
beta1_pelagic[1] 1.026 0.794 0.039 0.917 2.899
beta1_pelagic[2] 0.371 0.370 0.015 0.269 1.386
beta1_pelagic[3] 0.973 0.537 0.351 0.837 2.654
beta1_pelagic[4] 1.111 0.513 0.454 1.023 2.451
beta1_pelagic[5] 0.601 0.652 0.016 0.414 2.305
beta1_pelagic[6] 1.189 0.610 0.282 1.106 2.606
beta1_pelagic[7] 2.354 1.858 0.201 1.690 6.762
beta1_pelagic[8] 1.026 1.338 0.020 0.503 5.184
beta1_pelagic[9] 1.489 0.795 0.403 1.322 3.461
beta1_pelagic[10] 0.898 0.992 0.025 0.506 3.632
beta1_pelagic[11] 3.719 0.971 2.191 3.642 6.083
beta1_pelagic[12] 3.146 0.350 2.482 3.137 3.850
beta1_pelagic[13] 2.297 0.530 1.463 2.221 3.582
beta1_pelagic[14] 3.972 0.679 2.794 3.932 5.468
beta1_pelagic[15] 2.434 0.269 1.896 2.440 2.951
beta1_pelagic[16] 3.534 0.686 2.399 3.457 5.078
beta2_pelagic[1] 1.847 2.299 -3.362 1.711 6.562
beta2_pelagic[2] 2.358 2.706 -2.581 2.157 8.053
beta2_pelagic[3] 1.637 1.732 0.069 0.925 6.188
beta2_pelagic[4] 2.177 1.664 0.193 1.764 6.443
beta2_pelagic[5] 0.303 3.164 -6.188 0.264 6.340
beta2_pelagic[6] 2.279 1.937 0.102 1.863 6.846
beta2_pelagic[7] -2.509 1.710 -6.448 -2.525 -0.239
beta2_pelagic[8] -1.483 2.698 -6.805 -1.445 4.884
beta2_pelagic[9] 1.834 1.817 0.065 1.209 6.211
beta2_pelagic[10] 1.234 2.113 -3.431 0.791 6.100
beta2_pelagic[11] 0.207 0.150 0.088 0.184 0.424
beta2_pelagic[12] 1.060 0.431 0.519 0.984 2.064
beta2_pelagic[13] 0.833 0.846 0.177 0.567 3.432
beta2_pelagic[14] 0.352 0.176 0.168 0.313 0.789
beta2_pelagic[15] 1.987 1.047 0.830 1.694 4.890
beta2_pelagic[16] 0.488 0.403 0.164 0.352 1.844
beta3_pelagic[1] 24.895 4.427 19.725 23.154 36.260
beta3_pelagic[2] 28.808 4.957 20.293 28.998 38.060
beta3_pelagic[3] 30.227 3.141 24.037 30.232 37.191
beta3_pelagic[4] 25.697 2.118 21.316 25.778 30.393
beta3_pelagic[5] 28.588 4.797 20.543 28.476 38.237
beta3_pelagic[6] 30.314 3.443 24.807 30.301 37.663
beta3_pelagic[7] 26.421 3.519 19.750 26.598 32.635
beta3_pelagic[8] 26.942 4.836 20.132 26.436 37.753
beta3_pelagic[9] 29.856 4.443 21.786 30.119 37.337
beta3_pelagic[10] 27.837 4.995 19.514 27.659 38.068
beta3_pelagic[11] 38.106 2.390 33.027 38.321 41.786
beta3_pelagic[12] 41.866 0.151 41.461 41.911 41.996
beta3_pelagic[13] 40.741 1.147 37.823 41.008 41.958
beta3_pelagic[14] 40.652 1.184 37.773 40.971 41.956
beta3_pelagic[15] 41.816 0.187 41.310 41.873 41.996
beta3_pelagic[16] 40.792 1.142 37.678 41.131 41.966
mu_beta0_pelagic[1] 0.646 0.809 -1.077 0.697 1.964
mu_beta0_pelagic[2] 1.314 0.481 0.267 1.341 2.150
mu_beta0_pelagic[3] 0.116 0.505 -0.889 0.145 1.004
tau_beta0_pelagic[1] 3.436 9.634 0.047 1.379 18.198
tau_beta0_pelagic[2] 3.012 4.597 0.189 1.711 14.872
tau_beta0_pelagic[3] 1.551 1.139 0.182 1.283 4.434
beta0_yellow[1] -0.430 0.235 -0.962 -0.402 -0.066
beta0_yellow[2] 0.363 0.237 -0.278 0.397 0.715
beta0_yellow[3] -0.391 0.205 -0.799 -0.382 -0.062
beta0_yellow[4] 0.416 0.500 -0.685 0.507 1.127
beta0_yellow[5] -1.753 0.506 -2.682 -1.766 -0.698
beta0_yellow[6] 0.094 0.413 -0.602 0.114 0.781
beta0_yellow[7] 0.480 1.074 -2.215 0.896 1.683
beta0_yellow[8] 0.844 0.560 -0.802 0.974 1.430
beta0_yellow[9] -0.043 0.588 -1.382 0.007 0.880
beta0_yellow[10] 0.716 0.221 0.285 0.721 1.140
beta0_yellow[11] -3.598 0.323 -4.206 -3.602 -2.931
beta0_yellow[12] -2.691 1.044 -4.266 -2.993 -1.061
beta0_yellow[13] -4.088 0.388 -4.859 -4.074 -3.386
beta0_yellow[14] -3.252 0.427 -4.032 -3.278 -2.372
beta0_yellow[15] -3.867 0.335 -4.606 -3.842 -3.256
beta0_yellow[16] -3.456 0.332 -4.066 -3.475 -2.771
beta1_yellow[1] 0.444 0.518 0.014 0.294 1.938
beta1_yellow[2] 1.289 0.494 0.689 1.190 2.851
beta1_yellow[3] 0.750 0.348 0.303 0.704 1.543
beta1_yellow[4] 2.364 1.111 0.864 2.190 4.833
beta1_yellow[5] 4.276 1.751 1.369 4.036 8.309
beta1_yellow[6] 2.994 1.635 0.547 2.657 7.046
beta1_yellow[7] 2.105 1.743 0.102 1.642 6.773
beta1_yellow[8] 2.393 1.773 0.128 2.014 6.646
beta1_yellow[9] 2.111 1.359 0.190 1.846 5.673
beta1_yellow[10] 2.413 0.631 1.358 2.348 3.847
beta1_yellow[11] 3.535 0.438 2.668 3.534 4.386
beta1_yellow[12] 2.077 1.349 0.091 2.122 5.301
beta1_yellow[13] 3.396 0.607 2.415 3.343 4.634
beta1_yellow[14] 3.494 0.911 2.170 3.357 6.092
beta1_yellow[15] 2.913 0.448 2.123 2.891 3.870
beta1_yellow[16] 3.128 0.440 2.276 3.133 3.999
beta2_yellow[1] -0.757 2.933 -6.470 -0.807 5.479
beta2_yellow[2] -2.139 1.841 -6.740 -1.644 -0.098
beta2_yellow[3] -2.306 1.793 -6.651 -1.895 -0.106
beta2_yellow[4] -0.657 1.208 -4.640 -0.175 -0.054
beta2_yellow[5] -3.215 1.849 -7.467 -2.936 -0.588
beta2_yellow[6] 2.747 2.084 -1.963 2.603 7.021
beta2_yellow[7] 0.222 3.099 -6.013 0.312 6.010
beta2_yellow[8] -1.764 2.681 -6.820 -1.700 4.690
beta2_yellow[9] 1.210 3.029 -5.735 1.488 6.672
beta2_yellow[10] -2.575 1.731 -6.710 -2.184 -0.372
beta2_yellow[11] -0.758 0.276 -1.427 -0.718 -0.355
beta2_yellow[12] 1.401 2.859 -4.688 1.439 6.880
beta2_yellow[13] -0.607 0.300 -1.322 -0.556 -0.196
beta2_yellow[14] -0.593 0.385 -1.491 -0.526 -0.112
beta2_yellow[15] -0.883 0.473 -1.959 -0.785 -0.379
beta2_yellow[16] -0.764 0.287 -1.454 -0.718 -0.353
beta3_yellow[1] 28.687 4.682 20.247 28.787 37.833
beta3_yellow[2] 29.344 1.824 25.598 29.083 33.391
beta3_yellow[3] 31.859 2.199 26.716 31.947 35.871
beta3_yellow[4] 29.737 3.706 22.414 29.519 36.565
beta3_yellow[5] 32.436 1.136 30.077 32.515 34.246
beta3_yellow[6] 37.808 3.326 26.064 38.582 40.853
beta3_yellow[7] 28.068 3.535 21.497 27.973 35.904
beta3_yellow[8] 29.294 3.587 21.688 29.686 35.793
beta3_yellow[9] 34.289 4.910 22.977 35.896 41.129
beta3_yellow[10] 29.395 1.094 27.017 29.432 31.711
beta3_yellow[11] 41.865 0.169 41.427 41.919 41.997
beta3_yellow[12] 31.023 2.524 29.036 29.745 37.836
beta3_yellow[13] 41.427 1.104 38.227 41.766 41.992
beta3_yellow[14] 41.238 1.683 35.322 41.814 41.995
beta3_yellow[15] 41.805 0.234 41.158 41.881 41.997
beta3_yellow[16] 41.837 0.241 41.314 41.906 41.996
mu_beta0_yellow[1] -0.012 0.422 -0.798 -0.028 0.855
mu_beta0_yellow[2] 0.017 0.589 -1.284 0.063 1.043
mu_beta0_yellow[3] -3.324 0.611 -4.204 -3.445 -1.798
tau_beta0_yellow[1] 4.904 6.742 0.213 2.848 22.637
tau_beta0_yellow[2] 0.956 0.892 0.097 0.728 3.259
tau_beta0_yellow[3] 12.325 30.186 0.097 2.097 94.911
beta0_black[1] -0.076 0.157 -0.380 -0.078 0.229
beta0_black[2] 1.675 0.349 0.708 1.753 2.074
beta0_black[3] 1.192 0.286 0.573 1.240 1.547
beta0_black[4] 1.810 0.431 0.520 1.899 2.319
beta0_black[5] 1.439 1.139 -0.510 1.387 3.485
beta0_black[6] 1.387 1.108 -0.692 1.377 3.183
beta0_black[7] 1.390 1.131 -0.632 1.370 3.184
beta0_black[8] 1.164 0.309 0.457 1.204 1.648
beta0_black[9] 1.681 0.485 0.745 1.667 2.556
beta0_black[10] 1.363 0.151 1.070 1.368 1.644
beta0_black[11] 3.317 0.285 2.621 3.361 3.709
beta0_black[12] 4.405 0.211 4.000 4.416 4.786
beta0_black[13] -0.074 0.246 -0.564 -0.067 0.378
beta0_black[14] 1.867 0.632 0.208 2.030 2.691
beta0_black[15] 1.003 0.426 -0.159 1.096 1.515
beta0_black[16] 3.335 0.944 0.938 3.634 4.369
beta2_black[1] 3.136 1.733 0.791 2.795 7.376
beta2_black[2] -1.600 2.421 -6.605 -1.364 3.990
beta2_black[3] -0.175 3.168 -6.124 -0.038 6.025
beta2_black[4] -1.962 1.833 -6.364 -1.442 -0.058
beta2_black[5] 0.034 3.128 -6.141 0.081 6.191
beta2_black[6] -0.056 3.147 -6.372 -0.026 6.128
beta2_black[7] -0.137 3.103 -6.297 -0.162 5.740
beta2_black[8] -3.060 2.097 -7.418 -2.974 0.029
beta2_black[9] -1.302 2.394 -6.427 -0.918 4.019
beta2_black[10] -0.973 2.784 -6.198 -1.116 5.400
beta2_black[11] -1.722 2.220 -6.474 -1.479 3.271
beta2_black[12] -2.918 1.563 -6.633 -2.582 -0.755
beta2_black[13] -2.053 1.457 -5.847 -1.642 -0.365
beta2_black[14] -1.007 1.389 -5.164 -0.387 -0.079
beta2_black[15] -1.643 2.100 -6.402 -1.170 2.670
beta2_black[16] 1.853 2.178 -2.074 1.494 6.668
beta3_black[1] 41.820 0.791 40.113 41.905 43.131
beta3_black[2] 29.924 7.929 19.209 30.461 44.575
beta3_black[3] 27.949 7.450 19.229 27.252 44.297
beta3_black[4] 32.873 3.809 21.763 32.827 40.256
beta3_black[5] 32.010 7.354 19.844 32.061 45.189
beta3_black[6] 31.844 7.279 19.980 31.582 44.898
beta3_black[7] 31.940 7.284 19.825 31.669 44.630
beta3_black[8] 28.335 7.743 20.323 23.303 42.823
beta3_black[9] 34.284 8.271 19.593 35.258 45.260
beta3_black[10] 28.413 9.081 19.344 24.324 45.332
beta3_black[11] 33.989 4.342 29.118 32.781 44.828
beta3_black[12] 32.901 0.745 31.490 32.945 33.859
beta3_black[13] 39.208 0.909 37.141 39.325 40.517
beta3_black[14] 37.852 3.720 29.993 38.159 44.961
beta3_black[15] 35.873 5.032 29.188 35.010 45.293
beta3_black[16] 33.990 4.319 29.150 32.659 44.075
beta4_black[1] -0.285 0.204 -0.676 -0.291 0.124
beta4_black[2] 0.283 0.191 -0.090 0.280 0.664
beta4_black[3] -0.999 0.196 -1.391 -1.000 -0.623
beta4_black[4] 0.653 0.231 0.200 0.653 1.112
beta4_black[5] -0.015 3.236 -6.440 -0.041 6.421
beta4_black[6] 0.003 3.109 -6.117 0.041 5.981
beta4_black[7] -0.005 3.204 -6.442 -0.019 6.321
beta4_black[8] -0.854 0.384 -1.620 -0.842 -0.141
beta4_black[9] 2.137 1.110 0.296 2.007 4.680
beta4_black[10] 0.025 0.193 -0.356 0.022 0.413
beta4_black[11] -0.713 0.228 -1.165 -0.712 -0.266
beta4_black[12] 0.608 0.350 -0.077 0.600 1.310
beta4_black[13] -1.294 0.231 -1.759 -1.301 -0.835
beta4_black[14] -0.037 0.252 -0.530 -0.034 0.447
beta4_black[15] -0.936 0.228 -1.374 -0.934 -0.482
beta4_black[16] -0.582 0.251 -1.062 -0.584 -0.084
mu_beta0_black[1] 1.048 0.820 -0.730 1.092 2.423
mu_beta0_black[2] 1.341 0.646 0.073 1.369 2.325
mu_beta0_black[3] 2.015 1.103 -0.594 2.117 3.765
tau_beta0_black[1] 1.293 1.206 0.056 0.949 4.407
tau_beta0_black[2] 22.670 41.384 0.121 6.802 150.011
tau_beta0_black[3] 0.324 0.232 0.029 0.269 0.914
sigma_H[1] 0.223 0.048 0.139 0.219 0.328
sigma_H[2] 0.175 0.029 0.125 0.173 0.238
sigma_H[3] 0.185 0.041 0.114 0.183 0.273
sigma_H[4] 0.324 0.084 0.180 0.318 0.499
sigma_H[5] 1.014 0.218 0.624 1.001 1.474
sigma_H[6] 0.358 0.190 0.033 0.349 0.761
sigma_H[7] 0.292 0.058 0.201 0.284 0.431
sigma_H[8] 0.332 0.118 0.094 0.342 0.543
sigma_H[9] 0.521 0.125 0.325 0.503 0.798
sigma_H[10] 0.206 0.041 0.135 0.202 0.295
sigma_H[11] 0.272 0.045 0.197 0.269 0.376
sigma_H[12] 0.432 0.167 0.205 0.404 0.785
sigma_H[13] 0.217 0.037 0.154 0.213 0.297
sigma_H[14] 0.494 0.089 0.340 0.490 0.687
sigma_H[15] 0.246 0.040 0.180 0.243 0.331
sigma_H[16] 0.221 0.043 0.148 0.217 0.316
lambda_H[1] 3.496 5.063 0.155 1.933 15.996
lambda_H[2] 9.290 8.449 0.974 6.825 31.671
lambda_H[3] 6.642 9.702 0.302 3.644 31.266
lambda_H[4] 0.007 0.004 0.001 0.006 0.018
lambda_H[5] 2.374 6.861 0.018 0.489 19.400
lambda_H[6] 4.699 13.165 0.006 0.089 39.509
lambda_H[7] 0.016 0.011 0.002 0.013 0.044
lambda_H[8] 6.754 9.441 0.133 3.377 33.076
lambda_H[9] 0.016 0.011 0.003 0.014 0.045
lambda_H[10] 0.428 1.102 0.045 0.256 1.640
lambda_H[11] 0.277 0.434 0.011 0.125 1.292
lambda_H[12] 4.814 6.034 0.209 2.917 21.282
lambda_H[13] 3.717 3.327 0.254 2.747 13.107
lambda_H[14] 3.349 3.726 0.249 2.190 12.833
lambda_H[15] 0.040 0.642 0.003 0.017 0.103
lambda_H[16] 1.054 1.366 0.067 0.603 4.667
mu_lambda_H[1] 4.401 1.898 1.284 4.262 8.506
mu_lambda_H[2] 3.423 1.935 0.405 3.216 7.558
mu_lambda_H[3] 3.528 1.835 0.808 3.247 7.831
sigma_lambda_H[1] 8.730 4.193 2.213 8.205 18.032
sigma_lambda_H[2] 7.487 4.685 0.645 6.806 17.911
sigma_lambda_H[3] 6.220 3.906 1.052 5.347 16.030
beta_H[1,1] 6.951 1.048 4.484 7.114 8.508
beta_H[2,1] 9.897 0.457 8.883 9.915 10.763
beta_H[3,1] 7.995 0.756 6.138 8.099 9.176
beta_H[4,1] 11.139 7.594 -4.206 11.002 26.375
beta_H[5,1] -0.005 2.786 -5.653 0.106 5.273
beta_H[6,1] 2.123 4.518 -8.176 3.049 8.386
beta_H[7,1] 1.842 5.300 -9.422 2.106 11.558
beta_H[8,1] 1.082 3.431 -2.845 1.077 3.532
beta_H[9,1] 13.347 5.592 2.624 13.164 24.826
beta_H[10,1] 7.189 1.571 3.999 7.240 10.154
beta_H[11,1] 4.919 3.671 -3.274 5.749 9.987
beta_H[12,1] 2.615 1.009 0.806 2.521 4.898
beta_H[13,1] 9.074 0.944 7.212 9.150 10.498
beta_H[14,1] 2.173 1.010 0.229 2.188 4.197
beta_H[15,1] -6.093 3.775 -12.980 -6.323 1.956
beta_H[16,1] 3.142 2.291 -0.828 2.923 8.470
beta_H[1,2] 7.934 0.242 7.445 7.943 8.395
beta_H[2,2] 10.039 0.130 9.782 10.039 10.291
beta_H[3,2] 8.970 0.189 8.585 8.969 9.352
beta_H[4,2] 3.176 1.463 0.331 3.175 6.042
beta_H[5,2] 1.953 0.981 0.070 1.970 3.895
beta_H[6,2] 5.430 1.212 2.835 5.565 7.390
beta_H[7,2] 2.221 1.034 0.409 2.152 4.353
beta_H[8,2] 3.020 0.990 1.398 3.113 4.385
beta_H[9,2] 3.294 1.075 1.252 3.287 5.522
beta_H[10,2] 8.194 0.325 7.525 8.197 8.814
beta_H[11,2] 9.801 0.654 8.871 9.673 11.235
beta_H[12,2] 3.959 0.370 3.273 3.944 4.723
beta_H[13,2] 9.133 0.254 8.683 9.121 9.642
beta_H[14,2] 4.045 0.350 3.365 4.044 4.727
beta_H[15,2] 11.376 0.680 9.899 11.414 12.653
beta_H[16,2] 4.629 0.777 3.083 4.630 6.176
beta_H[1,3] 8.516 0.241 8.089 8.497 9.036
beta_H[2,3] 10.112 0.108 9.902 10.109 10.329
beta_H[3,3] 9.681 0.154 9.390 9.677 10.005
beta_H[4,3] -1.829 0.937 -3.644 -1.865 0.041
beta_H[5,3] 4.095 0.685 2.634 4.100 5.385
beta_H[6,3] 8.682 1.307 6.607 8.712 11.142
beta_H[7,3] -2.272 0.738 -3.775 -2.258 -0.876
beta_H[8,3] 5.385 0.493 4.704 5.312 6.405
beta_H[9,3] -2.494 0.732 -4.011 -2.480 -1.092
beta_H[10,3] 8.725 0.263 8.205 8.719 9.254
beta_H[11,3] 8.544 0.291 7.914 8.573 9.054
beta_H[12,3] 5.297 0.316 4.572 5.335 5.811
beta_H[13,3] 8.871 0.177 8.515 8.876 9.200
beta_H[14,3] 5.781 0.269 5.209 5.798 6.267
beta_H[15,3] 10.384 0.314 9.769 10.380 11.009
beta_H[16,3] 6.557 0.500 5.484 6.591 7.403
beta_H[1,4] 8.326 0.181 7.941 8.342 8.638
beta_H[2,4] 10.189 0.108 9.963 10.195 10.384
beta_H[3,4] 10.185 0.153 9.861 10.193 10.458
beta_H[4,4] 11.977 0.471 11.080 11.968 12.916
beta_H[5,4] 5.994 0.882 4.555 5.891 7.893
beta_H[6,4] 6.833 0.980 4.828 6.934 8.350
beta_H[7,4] 8.116 0.351 7.415 8.114 8.801
beta_H[8,4] 6.870 0.317 6.355 6.831 7.572
beta_H[9,4] 7.169 0.467 6.262 7.164 8.117
beta_H[10,4] 7.883 0.230 7.461 7.876 8.368
beta_H[11,4] 9.419 0.197 9.033 9.424 9.806
beta_H[12,4] 7.165 0.209 6.767 7.163 7.605
beta_H[13,4] 9.077 0.145 8.791 9.080 9.350
beta_H[14,4] 7.779 0.216 7.366 7.778 8.220
beta_H[15,4] 9.517 0.231 9.062 9.519 9.983
beta_H[16,4] 9.309 0.207 8.927 9.300 9.743
beta_H[1,5] 9.001 0.147 8.698 9.004 9.286
beta_H[2,5] 10.793 0.090 10.617 10.791 10.977
beta_H[3,5] 10.914 0.154 10.633 10.907 11.229
beta_H[4,5] 8.444 0.399 7.639 8.444 9.224
beta_H[5,5] 5.280 0.731 3.561 5.383 6.443
beta_H[6,5] 8.983 0.682 7.927 8.867 10.430
beta_H[7,5] 6.854 0.330 6.216 6.854 7.527
beta_H[8,5] 8.254 0.190 7.908 8.250 8.622
beta_H[9,5] 8.237 0.478 7.302 8.238 9.197
beta_H[10,5] 9.990 0.217 9.558 9.989 10.398
beta_H[11,5] 11.481 0.225 11.047 11.479 11.921
beta_H[12,5] 8.491 0.193 8.119 8.485 8.881
beta_H[13,5] 10.021 0.130 9.765 10.018 10.286
beta_H[14,5] 9.201 0.223 8.785 9.199 9.670
beta_H[15,5] 11.156 0.245 10.666 11.157 11.613
beta_H[16,5] 9.943 0.163 9.604 9.947 10.248
beta_H[1,6] 10.175 0.193 9.830 10.159 10.602
beta_H[2,6] 11.506 0.107 11.297 11.507 11.717
beta_H[3,6] 10.818 0.149 10.493 10.826 11.086
beta_H[4,6] 12.806 0.694 11.408 12.801 14.190
beta_H[5,6] 5.944 0.675 4.697 5.904 7.373
beta_H[6,6] 8.529 0.763 6.595 8.703 9.620
beta_H[7,6] 9.750 0.542 8.691 9.757 10.844
beta_H[8,6] 9.487 0.235 9.045 9.495 9.909
beta_H[9,6] 8.444 0.775 6.990 8.417 10.002
beta_H[10,6] 9.591 0.284 8.974 9.610 10.084
beta_H[11,6] 10.835 0.338 10.100 10.857 11.431
beta_H[12,6] 9.367 0.249 8.907 9.356 9.902
beta_H[13,6] 11.047 0.167 10.744 11.042 11.379
beta_H[14,6] 9.823 0.274 9.274 9.830 10.361
beta_H[15,6] 10.835 0.425 9.985 10.839 11.657
beta_H[16,6] 10.556 0.222 10.073 10.574 10.956
beta_H[1,7] 10.927 0.853 8.848 11.011 12.342
beta_H[2,7] 12.189 0.408 11.371 12.190 12.998
beta_H[3,7] 10.586 0.627 9.195 10.651 11.690
beta_H[4,7] 2.634 3.532 -4.403 2.665 9.752
beta_H[5,7] 6.664 2.360 2.508 6.447 12.151
beta_H[6,7] 9.722 2.930 4.760 9.425 17.410
beta_H[7,7] 10.918 2.702 5.549 10.925 16.319
beta_H[8,7] 10.871 0.841 9.444 10.830 12.598
beta_H[9,7] 4.638 3.969 -3.603 4.769 12.062
beta_H[10,7] 9.652 1.298 7.265 9.557 12.583
beta_H[11,7] 11.124 1.673 8.059 11.015 14.970
beta_H[12,7] 10.014 0.912 7.984 10.085 11.594
beta_H[13,7] 11.650 0.758 9.954 11.752 12.805
beta_H[14,7] 10.377 0.929 8.361 10.433 11.978
beta_H[15,7] 12.177 2.215 7.883 12.160 16.691
beta_H[16,7] 12.155 1.162 10.283 11.977 14.888
beta0_H[1] 8.906 13.555 -16.592 8.669 36.071
beta0_H[2] 10.636 5.902 -1.401 10.645 22.844
beta0_H[3] 9.868 9.516 -9.508 9.918 28.465
beta0_H[4] 6.356 178.703 -356.690 5.742 372.103
beta0_H[5] 4.194 35.971 -66.649 4.277 77.236
beta0_H[6] 9.185 62.477 -123.036 7.879 147.454
beta0_H[7] 6.551 120.368 -238.493 5.720 246.966
beta0_H[8] 5.948 29.237 -20.572 6.612 28.071
beta0_H[9] 5.891 115.540 -231.519 7.996 231.326
beta0_H[10] 7.843 30.129 -53.366 8.550 63.702
beta0_H[11] 9.015 49.670 -97.051 9.415 112.217
beta0_H[12] 6.803 10.746 -13.888 6.657 28.410
beta0_H[13] 9.859 11.376 -9.879 10.002 28.794
beta0_H[14] 7.216 11.289 -15.913 7.049 31.955
beta0_H[15] 10.465 103.853 -189.476 8.717 222.655
beta0_H[16] 8.006 21.402 -37.371 8.216 52.250